I’m in the US and have never heard of such a thing. If you’re sick on vacation then that’s not eligible for sick leave.
I suspect this varies by state, but the idea that sick leave for teachers is lacking has never been a common theme for any of the teachers in my family.
For the rest of the world, the idea that an employer can arbitrarily decide it is not possible for someone to be ill more than a certain number of days per year is bonkers.